Simulation and optimization of 30.17% high performance N-type TCO-free inverted perovskite solar cell using inorganic transport materials

Perovskite solar cells (PSCs) have gained much attention in recent years because of their improved energy conversion efficiency, simple fabrication process, low processing temperature, flexibility, light weight, and low cost of constituent materials when compared with their counterpart silicon based solar cells. Besides, stability and toxicity of PSCs and low power conversion efficiency have been an obstacle towards commercialization of PSCs which has attracted intense research attention. In this research paper, a Glass/Cu2O/CH3NH3SnI3/ZnO/Al inverted device structure which is made of cheap inorganic materials, n-type transparent conducting oxide (TCO)-free, stable, photoexcited toxic-free perovskite have been carefully designed, simulated and optimized using a one-dimensional solar cell capacitance simulator (SCAPS-1D) software. The effects of layers’ thickness, perovskite’s doping concentration and back contact electrodes have been investigated, and the optimized structure produced an open circuit voltage (Voc) of 1.0867 V, short circuit current density (JSC) of 33.4942 mA/cm2, fill factor (FF) of 82.88% and power conversion efficiency (PCE) of 30.17%. This paper presents a model that is first of its kind where the highest PCE performance and eco-friendly n-type TCO-free inverted CH3NH3SnI3 based perovskite solar cell is achieved using all-inorganic transport materials.


Device structure and simulation
There are different types of software used for simulation of solar cells such as PC1D, ASA, Amps-1D, WxAMPS, SCAPS-1D, SETFOS, Gpvdm, AFORS-het, Aspin-2D, PECSIM, Adept, TCAD, Atlas, Silvaco etc.However, SCAPS-1D software is used in this work to simulate an inverted tin-based perovskite solar cell with planar heterojunction because of its best accurate non-commercial tool that is straightforward in operation, with friendly dialog box and extremely quick in simulations at no additional expense and support for multi-junction solar cells 48 .Three related differential equations were solved to determine the energy bands, quantum efficiency of the device, current density-voltage (J-V) curve, and recombination rate curve.The Poisson Eq. (1), the electron continuity Eq. ( 2), and the hole Eq. (3) are built in the SCAPS-1D software.These curves are used to compute the solar cell device's open circuit voltage (V oc ), short circuit current density (J SC ), fill factor (FF), and power conversion efficiency (PCE). (1)

Background and selection of device parameters
Light generates electron-hole pairs within the absorber layer.The junction field draws holes to the HTM layers and electrons to the ETM layers, respectively.The thickness, coefficient of absorption, and mobility of the active material all affect the device's J SC .The photocurrent will increase as the absorption coefficient increases 49,54,55 .Another important consideration is the absorber's thickness, which must be sufficient to absorb the maximum cutoff wavelength of the incident solar light 49,53 .Aside from that, mobility is essential to achieving the high J SC which is ideally equal to the current in the solar cell.For the sample of CH 3 NH 3 SnI 3 produced using the open tube approach, a very high mobility of electrons (2000 cm 2 /Vs) and holes (300 cm 2 /Vs) was discovered by Ma et al. and Stoumpos et al. 56,57 .Lazemi et al. reported a high value of J SC using similar values of carrier mobility 53 .Devi et al. 58 and Khattak et al. 59 have taken into account the equal and noticeably lesser values of the electron and hole mobility, which are 1.6 cm 2 /Vs and 0.16 cm 2 /Vs respectively.In line with experimental work done by 60 , the electron (2000 cm 2 /Vs) and hole (300 cm 2 /Vs) mobility values for CH 3 NH 3 SnI 3 is adopted for use in this study.It is important to note that diffusion length also has a proportionality relationship to the square root of mobility 58 .
The device simulation was conducted under the 1000 W/m 2 light illumination at 300 K temperature and 1.5G air mass.The proposed device's series resistance was adjusted to 1 Ωcm 2 while the shunt resistance at 10 4 Ωcm 2 during simulation.The value of work function for front electrode (Cu 2 O) is 5.0 eV while the surface recombination velocity for electrons and holes as 10 5 cm/s and 10 7 cm/s respectively.Moreover, the work function for the back contact electrode ticked as flat band with surface recombination velocity for electrons and holes as 10 7 cm/s and 10 5 cm/s respectively at the beginning of the simulation until an optimized back contact electrode work function was determined as discussed in section "Effect of back contact electrode on the proposed inverted perovskite solar cell".The characteristics of the device's material parameters adopted were carefully selected from theories, experiments and research reviews is presented in Table 1, while the interface parameters are presented in Table 2. Scientifically, the neutral defect type adopted in the simulation means non-reactive, which can further be explained as a situation where there is no donor nor acceptor of charges within the films of a layer or interface.The bulk defect densities of the materials were chosen above ideal values to demonstrate ideal experimental conditions.
Various decisive parameters like electron mobility, hole mobility, carrier diffusion length, interfacial resistance, etc., have been considered constant and taken from the literature.These parameters are extremely dependent on experimental processes and can hugely alter practical performance of the device.The relative humidity, temperature, the type of instruments used, procedural and human expertise, control of crystallization and grain growth rates are some of the factors behind the real-life performance and their variations from theoretical values.

Results and discussions
In general, the electron and hole pairs are produced within the absorber layer after illumination.The junction field causes holes and electrons to travel in the directions of HTM and ETM layers, respectively.A voltage is created when these holes and electrons are collected at the anode and cathode, respectively.The simulation results of the proposed inverted device structure Cu 2 O/CH 3 NH 3 SnI 3 /ZnO using the available initial device parameters as contained in Tables 1 and 2 shows the J-V characteristics of the proposed device as shown in Fig. 1 produced a Voc of 0.9854 V, J SC of 30.4185 mA/cm 2 , an FF of 82.48% and PCE of 24.72%.The proposed device structure Cu 2 O/MASnI 3 /ZnO underwent further simulation and optimization so as to obtain optimized thickness of the constituent layers.

Effect of back contact electrode on the proposed inverted perovskite solar cell
Various metal back contact electrodes such as aluminium (4.26 eV), tin (4.42 eV) graphene (4.60 eV), silver (4.74 eV), iron (4.81 eV) and copper (5.00 eV) have been tested on the proposed inverted structure so as to determine the most appropriate one to be used for enhanced optimal performance.Figure 1 shows the work function of various metals used as back contact electrodes and their associated photovoltaic parameters on the proposed IPSC based device simulated using initial given parameters presented in Tables 1 and 2. The results in Fig. 1 clearly show that the choice of aluminum (Al) for back electrode maintained the most optimal device performance, as the V oc , J SC , FF and PCE of 0.9854 V, 30.4185 mA/cm 2  produced.It is interesting to note in this model that the J SC (Fig. 1b) remains constant as the work function of the back contact varies while the V OC , FF and PCE declines as the work function increases from 4.26 to 5.00 eV (Fig. 1a,c,d).For p-n configuration, the current is negative because of the uphill diffusion of the minority charge carriers in terms of concentration gradient arising from reverse bias during solar illumination.The current growth from the negative quadrant towards the positive quadrant signifies power generation up to zero value of current where an open circuit voltage (V OC ) of 0.9854 V is achieved.The J-V characteristics of the device having used aluminum as the back contact electrode is shown as Fig. 2.

Effect of n-type TCO-free on inverted perovskite solar cell architecture.
There is no experimental result for this exact structure (Cu 2 O/CH 3 NH 3 SnI 3 /ZnO/Al) known to us, which makes this research novel and interesting.There is no clear reasons why the lack of experimental works to support this study, but this could be due to lack of good conductivity of all-inorganic transport materials in nano electronics compared to organic transport materials and high processing temperature required.However, there are few simulation results of exact combination in n-i-p structure reported in 63,64 .The PCEs of 26.55% and 9.27% respectively were obtained in 63 and 64 , while our designed n-type TCO-free p-i-n device produced a superior PCE of 30.17% as shown in Fig. 8.The proposed inverted model will not simulate when the conventional n-type TCO (ITO/FTO) of donor concentration ND is used with the acceptor concentration NA being zero, except an organic p-type TCO is used which is outside the scope of this study.It's worth noting that the top transparent glass used as presented in Fig. 16 is an n-type TCO-free substrate in order to avoid non-convergence of voltage between the front and back electrodes when a conventional n-type TCOs are used.The carefully chosen transparent glass substrate size of 50 nm is not included in the simulation model, hence it is undoped and may not have significant impact on the device in real experimental situation.In this work, it is difficult to drive an output from the device if a Table 1.Parameters for modeling and simulation of an inverted planar perovskite solar cell structure using CH 3 NH 3 SnI 3 , CU 2 O and ZnO as Absorber, HTM and ETM respectively.Bandgap energy Eg (eV) 2.17 61 1.3 62 3.3 63 Electron affinity χ (eV) 3.2 61 4.17 62 4.0 63 Relative Permittivity ∈ r 7.5 63 6.5 63 9.0 63 Effective conduction band density CB (1/cm 3 ) 2.0 × 10 1863 1.0 × 10 1863 2 × 10 1863 Effective valence band density VB (1/cm 3 ) 1.8 × 10 1863 1.0 × 10 1963 1.8 × 10 1963 Electron thermal velocity (cm/s) 1 × 10 0761 1 × 10 0762 1 × 10 0736 Hole thermal velocity (cm/s) 1 × 10 0761 1 × 10 0762 1 × 10 0736 Electron mobility µn (cm 2 /Vs) 20 63 2000 60 100 63 Hole mobility µp (cm 2 /Vs) 80 63 300 60 25 63 Shallow uniform donor density ND (1/cm    www.nature.com/scientificreports/ The use of Cu 2 O as front contact electrode may suffer setback due its high sheet resistance and poor conductivity when compared to n-type TCOs.However, the sheet resistance of most metal oxides depends on the method of deposition, temperature, oxygen flow rate and thickness of the films.The control of power and oxygen flow rates during deposition of copper oxide thin films at a thickness of less than 100 nm prepared by reactive magnetron sputtering can reduce the sheet resistance and enhance performance of the device in practical sense 65 .The provision of a high density of low energy sputtered copper radicals/ions, and when combined with a controlled amount of oxygen, can produce good quality p-type transparent Cu 2 O films with electrical resistivity ranging from 10 2 to 10 4 Ω-cm 66 which makes Cu 2 O a potential transparent front conducting oxide for photovoltaic applications.Also, the doping of Cu 2 O with nickel can improve its p-type conductivity via extrinsic doping and post-growth processing 67 .Therefore, the Cu 2 O may not be as conductive as other n-type TCOs in experimental sense but runs conveniently in the simulation model without challenge which means the proposed n-type TCO-free model is novel and less complex, providing good direction in the design and modeling of simple inverted perovskite solar cells as shown in Figs. 13 and 16.Cu 2 O can act as a front electrode efficiently provided its thickness is thin enough to ensure adequate clarity and transparency to enhance admittance of photons into the absorber (perovskite) layer.

Effect of thickness of the HTM (Cu 2 O), absorber (CH 3 NH 3 SnI 3 ) and ETM (ZnO) layers
In this study, the variation of HTM's layer thickness from 10 to 100 nm results to a slight increase in FF (Fig. 3c) while a decline in device parameters such as V OC , J SC and PCE is experienced as presented in Fig. 3a,b,d respectively.
The thickness of the absorber layer considerably affects the solar cell's overall performance.The increase in absorber's thickness decreases the V OC due to increase in series resistance.Meanwhile, the increase in absorber's thickness increases the J SC, FF and PCE to the maximum after which it decreases with further increase in thickness.In this study, the thickness of CH 3 NH 3 SnI 3 has been adjusted in this simulation from 100 to 1500 nm.The fluctuation of photovoltaic characteristics with thickness of absorber layer is shown in Fig. 4. The V OC declines as a result of faster recombination due to increased thickness (Fig. 4a).A thicker absorber layer absorbs more photons, which increases short circuit current density (J CS ) and the fill factor (FF) and as seen in Fig. 4b,c, respectively.The solar cell efficiency is increased as the thickness of absorber layer increases up to an ideal thickness for the solar cell after which efficiency declines (Fig. 4d).However, as diffusion necessitates a longer charge travel distance, recombination is more common in larger absorber layers; hence, efficiency decreases after a certain thickness value.Our results concur with experimental findings in 62,68 .As shown in Fig. 4d, the ideal absorber layer thickness for this inverted PSC is achieved between 1200 and 1300 nm.
Nevertheless, the increase in ETM's thickness leads to a non-noticeable change in V OC , J SC , FF and PCE (Fig. 5a-d) respectively.Therefore, it can be inferred that while device performance is mostly determined by absorber thickness, IPSC device performance is not influenced by the ETM layer's thickness but rather varies slightly with the HTM's thickness, which is designed to be small enough to guarantee optical transparency and ensure easy photon penetration to the absorber layer.The selection of optimal thickness is important to regulate series and shunt resistance and ensure improved device performance in terms of short circuit current, open circuit voltage, fill factor and power conversion efficiency.The simulation of these optimized dimensions led to an improvement in the solar cell parameters as it produced a Voc of 0.9633 V, J SC of 33.8049 mA/cm 2 , FF of 82.84% and PCE of 26.97% as shown in the J-V characteristics curve (Fig. 6).www.nature.com/scientificreports/

Effect of absorber's doping concentration (NA)
The holes' acceptor density of the absorber layer has a major impact on the photovoltaic cell's device performance in addition to its thickness.As demonstrated in Fig. 7, the Fermi energy level of the hole falls with increasing doping concentration of the acceptor, and as a result, V OC increases (Fig. 7a).Also, an increase in the doping concentration of the acceptor leads to a built-in potential that increases charge separation, which in turn causes a rise in V OC .In this work, the acceptor concentration NA (1/cm 3 ) of the absorber layer is varied within a range of 3 × 10 14 cm −3 to 3 × 10 21 cm −3 to ascertain the most optimal value that can produce an optimal performance of the proposed device.Nevertheless, J SC maintains a steady decline marginally up to NA's value of 3 × 10 19 cm −3 before falling off sharply.At the same NA's value, the value of FF drops suddenly which might be caused by a rise in the rate at which charge carriers within the absorber layer recombine or an increase in series resistance 55 .
The absorber layer's doping concentration value of 3 × 10 19 cm −3 produced the best cell performance having V oc of 1.0867 V, J SC of 33.4942 mA/cm 2 , FF of 82.88% and PCE of 30.17% as shown in Fig. 7a-d respectively, while its J-V characteristics is shown as Fig. 8.The complex nature of an organic molecule in the A site of the perovskite structure (ABX 3 ) may be the cause of degradation, as evidenced by the absorber's bandgap of 1.3 eV and the measured Voc of 1.0867 V. Using varying ratios of the precursors causes an intrinsic fault when the perovskite structure is distorted.Higher degrees of crystallization and a slower rate of breakdown are the results of vacancies in the structure caused by the excess CH 3 NH 3 I (MAI).The crystalline lattice's anomalies emphasize the role MAI plays in the deterioration process.Excess MAI may potentially release halide ions, depending on the concentration.Afterwards, these halide ions function as dopants, altering the perovskite semiconductors' bandgap 69 .When exposed to air, the Sn 2+ in CH 3 NH 3 SnI 3 is changed to Sn 4+ (a process known as self-doping), converting the device into a p-type semiconductor.Sadly, this procedure deteriorates the device performance, such as the output power and the power conversion efficiency 56,70 .

Effect of series resistance R series and shunt resistance R shunt
The resistance in series and shunt (R series and R shunt ) affects the J-V curve's form and slope, which in turn affects the solar cell's efficiency.The connections electrodes, electrical dissipation in the perovskite, and layers of hole and electron transport materials (HTM and ETM) are primarily linked to the cause of the R series .However, different recombination pathways, device design, and defects induced during the layer deposition process are linked to the cause of the R shunt .According to the literature, a high shunt resistance and a low series resistance are necessary for a solar cell to have a high efficiency.Electrons cannot flow freely across a circuit if the series resistance is large, and leakage current will occur if the shunt resistance is low, producing PSCs with low stability and efficiency.When there's a low shunt resistance or a high series resistance, the PSC's maximum output and FF would both drop 71,72 .The ideal diode model's Eq. ( 4) was applied in order to comprehend the impact of R series and R shunt on the perovskite solar cell's performance 73 .
When J ≈ 0 mA/cm 2 for open circuit state, the variables V OC and R shunt relationship is presented in Eq. (5) where J is the current flowing via the external circuit, V is the output voltage, A is the ideality factor, k is the Boltzmann constant, T is the temperature, q is the electron charge, J O is the saturation current density and J L is the light-induced current density.As a result, low R shunt reduces photovoltaic voltage and may also have an impact on the photocurrent that is collected, whereas high R series values primarily influence the FF and Jsc values 72 .
While keeping the other simulation parameters same, R series and R shunt were changed from 0 to 100 Ωcm 2 and 10 3 Ωcm 2 to 10 10 Ωcm 2 respectively, to better understand their influence on the J-V curves.The responses of V OC , J SC FF and PCE as a function of R series are presented in Fig. 9. V OC stays fairly constant, J SC falls from 33.51 to 10.77 mA/cm 2 , and FF drops from 85.63 to 24.88% while R series grows from 0 to 100 Ωcm 2 .As a result, as Fig. 9d illustrates, PCE's behavior is precisely proportional to J SC and FF, decreasing from 31.16 to 2.91% for the same range.Alternatively, as Fig. 10 illustrates, when R shunt rises from 10 3 to 10 10 Ωcm 2 , V OC rises from 1.0858 to 1.0868 V, J SC maintains a constant 33.49mA/cm 2 from 10 4 Ωcm 2 , FF rises from 80.75 to 83.12%, and the PCE (4) www.nature.com/scientificreports/rises from 29.34 to 30.26% respectively (Fig. 10a-d).For R series and R shunt , the optimal values are therefore 1 Ωcm 2 and 10 6 Ωcm 2 respectively, which is in conformity with literature.

Effect of the defect state of bulk and interface layers
The impact of the absorber's defect density is an important factor that needs to be examined.In the absorber layer, defects are inevitable.Both at surfaces and in the bulk, they are present.Point defects in the perovskite absorber layer include lattice vacancies, interstitial, Schottky, and Frenkel defects.In addition, there may be higher order defects like grain boundaries and dislocations 74 .The self-doping process in the absorber layer creates the p-type semiconductor that results in an impurity defect 54,56,75,76 .These defects cause the energy bandgap to appear at shallow or deep levels 74 .Charge carriers have the ability to capture and promote nonradiative recombination of  www.nature.com/scientificreports/electron-hole as a result of these defects 53,55 .Noteworthy, the simulated interface defect density for both electron and hole recombination velocities was 1 × 10 -2 cm/s for both HTM/MASnI 3 and ETM/MASnI 3 interface.In the Sn-based perovskite absorber layer, the electron and hole diffusion lengths were 16 µm and 6.2 µm, respectively.The optimized device's absorber defect density (Nt) of 2 × 10 15 cm −3 achieved a V OC of 1.0867 V, a J SC of 33.4942 mA/cm 2 , FF of 82.88%, and a PCE of 30.17%.Nevertheless, synthesizing a material with a low defect density value is a challenging task in an experiment 55 .The Shockley-Read-Hall (SRH) recombination model has been applied to provide understanding regarding the impact of defect density in the absorber layer on device performance 49,53,77 .The effect of defect density on the recombination rate based on the SRH recombination model is essential to determining the critical influence of Nt on the device performance.The plot of recombination rate with depth from the optimized device's surface is depicted in Fig. 11.
The proposed device produced quantum efficiency curve covering the entire visible spectrum (300-900 nm) achieving an optimum quantum efficiency (QE) of 99.38% at 580 nm wavelength, which is in agreement with other works 15,43,54,61,78,79 is presented as Fig. 12.The simulated inverted structure, energy band diagram, energy band alignment and complete device structure of the optimized inverted planar perovskite solar cells are presented as Figs.13, 14, 15 and 16, respectively.It's very clear that the photovoltaic performance of the proposed device as shown in Table 3 is superior to other related works reported in the literature.

Conclusion
The toxic-free CH 3 NH 3 SnI 3 as light harvesting material is explored in this study.A heterojunction planar perovskite solar cell with an inverted structure Glass/Cu 2 O/CH 3 NH 3 SnI 3 /ZnO/Al was simulated, optimized and analyzed in this paper.In relation to various photovoltaic parameters such as the work function of the back contact electrodes, thickness of the HTM layer, absorber and the ETM layers, and the absorber's doping concentration were optimized.The thickness of the HTM, absorber layer and ETM were optimized to 40 nm, 1200 nm and 200 nm respectively.The optimized structure produced an enhanced Voc of 1.0867 V, J SC of 33.4942 mA/cm 2 , FF of 82.88% and PCE of 30.17% respectively.The results indicate that an increase in doping concentration of the absorber increased the Voc, FF and PCE but decreased the J SC of the solar cell.The interface between the ETM/ back-electrode requires a cheap and low work function metal for enhanced performance.The n-type TCO-free inverted CH 3 NH 3 SnI 3 -based PSC provides a potential path to attaining simple, eco-friendly, cheap and highly efficient perovskite solar cell device using all-inorganic transport materials.
TCO of an n-type material (FTO/ITO) is used as front electrode in the inverted structure when the same n-type material of same polarity is used as back hole blocker (ZnO) because of non-voltage convergence arising from non-compatible work function between the layers.The non-voltage convergence experienced when ITO with metal function of 4.7 eV is used is as a result of non-ideal band gap between the adjacent semiconductors layers (ITO/Cu 2 O) which makes the proposed n-type TCO-free model feasible.However, a back contact electrode of low metal function lower than ZnO like aluminium (4.26 eV) is required for optimal performance.

Figure 1 .
Figure 1.Effect of different back metal contact electrodes on parameters of the proposed IPSC.(a) Plot of V OC against metal work function, (b) Plot of J SC against metal work function, (c) Plot of FF against metal work function, (d) Plot of PCE against metal work function.

Figure 2 .
Figure 2. J-V Characteristics of the proposed inverted perovskite solar cell with initial parameters using MASnI 3 as absorber material, Cu 2 O as HTM, ZnO as ETM and Al as back contact respectively.

Figure 3 .
Figure 3.Effect of variation of thickness of the HTM layer (Cu 2 O) on solar cell parameters.(a) Plot of V OC against thickness, (b) Plot of J SC against thickness, (c) Plot of FF against thickness, (d) Plot of PCE against thickness.

Figure 4 .
Figure 4. Effect of variation of thickness of the absorber layer (MASnI 3 ) on solar cell parameters.(a) Plot of V OC against thickness, (b) Plot of J SC against thickness, (c) Plot of FF against thickness, (d) Plot of PCE against thickness.

Figure 5 .
Figure 5.Effect of variation of thickness of the ETM layer (ZnO) on solar cell parameters.(a) Plot of V OC against thickness, (b) Plot of J SC against thickness, (c) Plot of FF against thickness, (d) Plot of PCE against thickness.

Figure 6 .
Figure 6.J-V characteristics of the optimized device's thickness using MASnI 3 as absorber material, Cu 2 O as HTM, ZnO as ETM and Al as back contact respectively.

Figure 7 .
Figure 7. Effect of variation of doping concentration of the absorber (CH 3 NH 3 SnI 3 ) on solar cell parameters.(a) Plot of V OC against doping concentration (NA), (b) Plot of J SC against doping concentration (NA), (c) Plot of FF against doping concentration (NA), (d) Plot of PCE against doping concentration (NA).

Figure 8 .
Figure 8. J-V Characteristics of the final optimized inverted simulated solar cell device using MASnI 3 as absorber material, Cu 2 O as HTM, ZnO as ETM and Al as back contact respectively.

Figure 9 .
Figure 9.Effect of series resistance variation on the optimized IPSC based device parameters.(a) Plot of V OC against series resistance.(b) Plot of J SC against series resistance.(c) Plot of FF against series resistance, (d) Plot of PCE against series resistance.

Figure 10 .
Figure 10.Effect of shunt resistance variation on parameters of the optimized IPSC device.(a) Plot of V OC against shunt resistance, (b) Plot of J SC against shunt resistance, (c) Plot of FF against shunt resistance, (d) Plot of PCE against shunt resistance.

Figure 11 .
Figure 11.Recombination rate of the optimized device with depth from the surface.

Figure 12 .
Figure 12.Quantum efficiency of the proposed inverted perovskite solar cell.

Figure 14 .
Figure 14.Energy band diagram of the proposed inverted perovskite solar cell.

Figure 15 . 7 Figure 16 .
Figure 15.Energy band alignment profile of the proposed inverted perovskite solar cell.

Table 2 .
Parameters of interface layer.

Table 3 .
Photovoltaic parameters of either Cu, Zn or Sn-based perovskite solar cells of some reported experimental and simulated works from the literature.